Quiz 1:Statistical Inference(Data Science Specialization):Answers2025

Question 1

Consider influenza epidemics… What is the probability that the mother has contracted influenza?

✅ 11%
❌ 17%
❌ 6%
❌ 5%

Explanation:
Use the union formula:
P(father ∪ mother) = P(father) + P(mother) − P(both).
0.17 = 0.12 + P(mother) − 0.06 ⇒ P(mother) = 0.17 − 0.12 + 0.06 = 0.11 (11%).

Question 2

X ~ Uniform(0,1). What is its 75th percentile?

❌ 0.25
❌ 0.50
✅ 0.75
❌ 0.10

Explanation:
For a Uniform(0,1) distribution, the p-th quantile is p. So the 75th percentile is 0.75.

Question 3

Coin game: heads with prob p, pay X on heads, receive Y on tails. Condition for game to be fair (expected earnings 0)?

❌ p1−p=XY\dfrac{p}{1-p} = \dfrac{X}{Y}1−pp​=YX​
✅ p1−p=YX\dfrac{p}{1-p} = \dfrac{Y}{X}1−pp​=XY​
❌ p=XYp = \dfrac{X}{Y}p=YX​
❌ $X=Y$

Explanation:
Your expected earning = $-(p)X+(1-p)Y=0$. Solve: $(1-p)Y=pX$ ⇒ YX=p1−p \dfrac{Y}{X} = \dfrac{p}{1-p}XY​=1−pp​. So the second option is correct.

Question 4

A symmetric density about 0 — what is its median?

✅ The median must be 0.
❌ The median must be 1.
❌ We can’t conclude anything.
❌ The median must be different from the mean.

Explanation:
Symmetry about 0 implies the distribution places equal mass on either side of 0, so the 50% quantile (median) is 0.

Question 5

Discrete PMF: x = 1:4, probs 0.1,0.2,0.3,0.4. What is the mean?

❌ 4
❌ 1
✅ 3
❌ 2

Explanation:
Mean = Σ x * p = 1·0.1 + 2·0.2 + 3·0.3 + 4·0.4 = 0.1 + 0.4 + 0.9 + 1.6 = 3.0.

Question 6

Pregnancy test: sensitivity 75%, specificity 52% (use lower value), prevalence 30%. What is P(pregnant | positive)?

❌ 20%
✅ 40%
❌ 10%
❌ 30%

Explanation:
Bayes’ rule:
P(preg | +) = sens·prev / (sens·prev + (1−spec)·(1−prev))
= 0.75·0.30 / (0.75·0.30 + 0.48·0.70) = 0.225 / 0.561 ≈ 0.40 (40%).

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